Method and structure for growing crystals

ABSTRACT

A MELT OR PUDDLE IS FORMED IN A SOLID MATERIAL CONTAINED IN A COLD CRUCIBLE. THE SOLID MATERIAL ACTS AS A SELF-CRUCIBLE FOR THE MELT AND CRYSTALS ARE GROWN AT THE CENTER OF THE MELT. THE MELT IS FORMED IN THE SOLID MATERIAL BY A MULTITUDE OF ARCS STRUCK BETWEEN THE MATERIAL   WHICH MAY ACT AS AN ANODE, AND A MULTITUDE OF CATHODES WHICH ARE DIRECTED TOWARD THE MATERIAL, SO THAT THE ELECTRON AND PLASMA FLOW FROM THE CATHODES TO THE MATERIAL, PRODUCES AND MAINTAINS THE MELT.

l2-O i- 71 XR 396259660 EED El AL T i RE FOR GROWING CRYSTALS Filed March 18, 1968 2 Shoots-Show. 1

CATHODE ELECTRODE ASSEMBLY 1 3| as r 36 45 l. 35 m: as 91 M- 3e 5 I a 2 2 42 7 5 I 5 630 l o E I 57 CATHODE 4| 6 s5 58 BALL"39 54 I SEED CRYSTAL 0R INGOT 3-4-5 E T P. I. ELECTRODE 72 4 m :5 SPYREX CYLINDER 2 ANODE CHARGE 23 GRAPHITE PISTON 2?|6 PLATE INVENTORS I 25 THOMAS B. REED EDWARD POLLARD ATTORNEY Dec. 7, 1971 B. REED ET AL 3,625,650

METHOD AND STRUCTURE FOR GROWING CRYSTALS Filed'March 18, 1968 2 Shoots-Shoot 3 'l I 3 I I 94 INVENTORS THOMAS B. REED EDWARD POLLAR ATTORN EY United tats 3,625,660 METHOD AND STRUCTURE FOR GROWING CRYSTALS Thomas B. Reed, Concord, and Edward R. Pollard, Arlington, Mass, assignors to Massachusetts Institute of Technology, Cambridge, Mass.

Filed Mar. 18, 1968, Ser. No. 713,955 Int. Cl. B01j 17/18 U.S. Cl. 23-301 SP 1 Claim ABSTRACT OF THE DISCLOSURE DISCLOSURE The invention described herein was made in the course of work performed under contract with the Electronic Systems Division, Air Force Systems Command, United States Air Force. The invention relates to methods and means for growmg crystals, and more particularly to are heating and crystal-growing techniques with novel means for forming and containing an arc-heated melt from which the crystal 1s grown.

Controlled crystal growth from a melt is presently accomplished by a number of techniques. In one of these techniques, the Czochralski technique, the crystals are pulled in the vertical direction from the center of a melt by inserting a pointed ingot or a seed crystal into the melt and then withdrawing in the vertical direction the ingot or seed crystal as the crystal or crystals grow on it. The seeds are used when the orientation of the grown crystal is to be predetermined and if no seed crystal is used, then the number of initial nuclei crystals can be minimized by using a pointed ingot and bringing the point of the ingot just in contact with the melt. In either case, the rate of pulling usually measured in centimeters per hour and the amount of heat are the main factors which control the crystal dimensions. Other techniques for the controlled growth of crystals from a melt employ molds into which liquid from a melt which is very uniform as to composition and temperature, fiows very rapidly and thereafter crystallizes to form a desired poly-crystalline structure.

Heretofore, the melt for such controlled crystal growth has been produced in a heated crucible of a material selected not to react with the melt. Some of the crucible materials that have been employed in the past are silica, alumina, graphite, silicon, carbide, aluminum nitride, boron nitride, tungsten, and a number of others. Most of these crucible materials are limited to use for growing crystals of metals with melting points below about 1500 C., and considerable care must be taken to obtain a crucible of pure material and to maintain it clean. Because of this limitation of the crucible, the Czochralski technique has in the past been limited to pulling crystals from melts at temperatures below 1500 C. Above that temperature, the floating zone melting technique or the Verneuil technique has been employed. Accordingly, it is one subject of the present invention to provide a method and structure for controlling the growth of crystals from. melts at temperatures in excess of 1500" C.

3,625,650 Patented Dec. 7, 1971 It is another object of the present invention to provide a method and structure for growing crystals as in the Czochralski technique from melts at temperatures in excess of 1500 C.

It is another object of the present invention to provide method and structure for producing a melt and controlling the growth of crystals from the melt, which avoids the necessity of heating the cucible containing the material to the same or higher temperature as the melt.

It is another object of the present invention to provide method and structure for forming a melt of substantially uniform composition and temperature from which crystals are grown.

It is another object of the present invention to provide method and structure for stirring the melt from which crystals are grown.

It is another object of the present invention to provide an arc-heated Czochralski crystal-growing device, which is not subject to contamination from a crucible.

It is anotherobject of the present invention to provide such an arc-heated Czochralski type crystal-growing device in which the melt is continually stirred to maintain uniform temperature and composition throughout, while crystals are pulled from the melt.

In accordance with features of the present invention, a charge of solid material, which may be in granular or powdered form, held in a cold crucible, serves as an anode and a plurality of cathodes are disposed above this material and energized so that arcs are struck between each of the cathodes and the material, the arcs being of sut'ricient intensity to melt a portion of the material to form a puddle of liquid contained by the solid material. The cathodes may be oriented so that the electron and plasma flow from each cathode to the melt causes a flow of fluid in the melt which stirs the melt, and crystals are pulled from substantially the center of the melt, employing the well-known Czochralski crystal-pulling technique.

In a particular embodiment described herein, three such cathodes are employed and arranged so that the direction lines of electron and plasma flow from the cathodes to the melt define tangents to a common circle, which are all in the same circular direction. This causes the liquid in the melt to flow in a circular pattern, stirring the melt, to maintain the temperature and composition thereof substantially uniform throughout. Means are also provided for injecting a purging gas over the top of the melt to clear the area of impurities and provide a suitable medium for the arcs.

Examples of the invention include an electrically conductive anode assembly having a cavity for containing the anode charge of selected material, a cathode assembly containing a plurality of moveable cathode probes disposed around a crysta-growing mechanism, which may include a seed crystal or a pointed ingot for pulling crystals from the melt and windows for observing the posi tions of the cathode probes and/or introducing doping materials to the melt. The cathode body is supported above the anode body by a transparent cylinder which may be Pyrex, and which seals to each body and permits viewing the growth process. The purging gas is introduced through the anode body.

Other objects and features of the invention will be apparent from the following specific description, taken in conjunction with the figures in which;

FIG. 1 is a cross-section view taken through the axis of an arc-heated Czochralski-type crystal-growing device incorporating features of the invention;

FIG. 2 is a top-sectional view of the device illustrating the arrangement of cathode electrodes and windows in the cathode body taken as shown in FIG. 1;

FIGS. 3 and 4 are top-sectional views taken as shown in FIG. 1 to reveal the orientation of the cathode probes, the crystal-pulling mechanism, the melt, and the means for injecting purging gas over the melt;

FIG. is a top-sectional view to illustrate structure and technique for providing a melt from a material of relatively low electrical conductivity and held in a cold crucible;

FIG. 6 is a three-quarter view of the complete device, showing ports for introducing cooling fluid and purging gas from external sources.

The present invention contemplates method and structure for pulling or growing crystals of both metal and nonmetal materials of either high or relatively low melting points, from a melt. This is accomplished by arc-heating solid material. The material may be in bulk, granular, or powered form. Crystals are pulled or grown from the melt. The arcs are controlled in such a way that only a portion of the material melts and this melt is contained by the rest of the material, and so the container for the melt'is the material itself in solid form and will not contaminate the melt in any manner.

The charge of material is heated by a number of arcs that are struck between the material which functions as an. anode and a plurality of cathodes arranged around the center of this anode, so that the electron and plasma flow from each cathode to the anode not only heats the material sufiiciently to form the melt, but also imposes a stirring action on the liquid in the melt, to maintain the melt temperature substantially uniform throughout. The crystals are pulled or grown from the center of the melt in the typical fashion, generally known as the Czochralski pulling technique. The mechanism for pulling the crystals may consist of a seed crystal or a pointed ingot which is movable toward and away from the melt, substantially at the center thereof. An inert gas may be played over the melt to purge the area around the melt of impurities and provide a medium for the arcs.

This method of pulling or growing crystals from a melt is conveniently performed employing three cathodes which are preferably moveable, elongated, electrically conductive bodies positioned just above the anode material and then energized so that arcs are struck between each cathode and the anode material. These arcs are of sulficient intensity to'melt a portion of the material so that the melt is contained in a pool atthe center of the material. Furthermore, the cathodes are oriented so that the electronand plasma flow from each to the melt causes liquid in the melt to circulate and thus, the liquid is stirred and the temperature of the melt is maintained uniform.

It has been found convenient to mount the cathode electrodes above the anode material, so that an operator can move them toward or away from the melt and can turn them to various angular positions relative to each other and relative to the melt. Since the top surface of the melt is globular in shape, and the cathode electrodes are directed toward this surface, it is convenient to locate the crystal-pulling mechanism along a vertical axis through the center of the globular surface and to dispose the numerous cathodes in a regular orientation about this axis. Three such cathodes are sufiicient to produce the melt in the anode material, and when these cathodes are oriented so that the electron and plasma flow from each to the anode melt is not in line with the axis, but in fact, defines tangents to acircle concentric with the axis, the arcs will produce a stirring effect in the melt, either clockwise or counter-clockwise, and this stirring effect will maintain the temperature and compostion of the melt uniform. When the melt is maintained uniform in this manner, crystals of uniform quality may be pulled or grown from the melt.

The above method for pulling or growing crystals has been employed quite effecively to grow uniform crystals of TiO, NbO, Sn, Nb, Cr, V, Ge, Vo, Cu O, Si, TiC, and Ti O Tin (Sn) melts at abotu 232 C. and titanium carbide (TiC) melts at about 3160 C. It will be recognized that such crystals of some of these materials cannot be pulled or grown employing the Czochralski type crystal-pulling devices known in the prior art, because no known crucible can contain the material.

The FIGS. 1 to 6 included herewith describe suitable structures for practicing the present invention. These structures are called herein arc-heated Czochralski crystal-puller devices, by which crystals are pulled in a vertical direction from a melt. FIG. 1 is a cross-section view of the device, the section being taken through the major axis 1 of the device. As will be seen from the description which will follow, many of the parts of this device are figures of revolution about the axis 1, and it will be quite obvious from the description which parts are figures of revolution and which parts are not.

As shown in. FIG. 1, the anode assembly 2 is substantially cylindrical in shape and disposed on the axis 1. The cathode assembly 3 also is of generally cylindrical shape, disposed above the anode assembly and connected thereto for support by a transparent Pyrex cylinder 4. The trans parent cylinder 4 seals to the anode body and cathode body by gaskets 5 and 6 respectively, and is held firmly against these gaskets by bolts such as 7 and 8, which extend through a base 9 which abuts the anode assembly, and into accommodating bosses 11 and 12 and cathode assembly. The base 9 is of electrically insulating material and so the cathode body and anode body are electrically isolated from each other and define in between the crystal-growing area 13, which can be viewed through the Pyrex cylinder 4.

The anode assembly 2 consists of a heavy anode cylinder 15 which may be made of copper. Into this anode cylinder is inserted the anode cooling sleeve 16, which contains a cavity 17 for circulating fluid to keep the anode body 2 from getting too hot. A second annular cavity 18, in the sleeve, conducts purging gas which may be argon with traces of hydrogen, from an external source for injection into the crystal-growing region 13, as will be described herein below.

The anode charge crucible 21 fits into the anode cooling sleeve 16 and may be tapered as shown, to facilitate removing, and at the same time provide good conductive contact with the sleeve. This crucible may be copper and has a bore 22 at the center, which is fitted with a copper or graphite piston 23 moveable along the axis 1 by moving the piston screw 24 along the axis. This is facilitated by turning the sleeve 25, which threadably connects with the screw. The sleeve 25 is rotatably attached to plate 26 by bearing 27, and this plate fits snugly into the bottom of bore 22, sealing against the bore by ring 28. The piston 23 fits snugly in the bore 22 so that it does not turn when the sleeve 25 is rotated. The anode charge 29 of bulk or powdered material in which the melt is to be formed is placed on top of the piston 23 and the piston is raised or lowered along the axis 1 by manipulating the sleeve 25 to vary the position along the axis 1 of the anode charge.

The cathode assembly 3 consists of an aluminum block 30 which has a generally cylindrical shape of a somewhat larger diameter than the diameter of the anode assembly. This block is equipped with an annular groove to accommodate the gasket 6 in registry with an annular groove in the anode body that accommodates the gasket 5, and these gaskets seal against the transparent cylinder 4, to space the anode and cathode assemblies apart defining the crystal growing region 13. The cathode block 30 supports the crystal-pulling mechanism 31, which is disposed in the block substantially along the axis 1, and three cathode electrode assemblies 32 to 34, equally spaced about the axis 1, each on its own axis, 35 to 37 respectively, which are generally toward the anode charge 29 and cross the axis 1. Since the cathode electrode assemblies, 32 to 34, are identical, the details only of assembly 32 will be described herein.

Cathode assembly 32 includes a bore 38 through the cathode block 30 on the axis 35. The bore 38 contains the cathode electrode pivot ball 39, which is held in place within the bore between electrically insulating rings 40 and 41. Ring 41 is held by a step in the bore, and ring 40 is held within the bore against the ball 39 by a nylon retaining ring 42, which screws into accommodating threads in the bore. The retaining ring 42 is adjusted so that the ball 39 is firmly held, but at the same time can rotate with three degrees of rotational freedom relative to the bore.

The cathode ball 39 holds the brass cathode electrode screw 43, which threadably screws through the center of the ball and this screw in turn holds the cathode electrode 44. The electrode 44 is preferably an elongated, sharp-pointed body of thoriated tungsten or thoriated tungsten-zirconium alloy.

Since the ball 39 has three degrees of rotational freeshows the position of the three electrodes, 44, 47 and 48,

which is accomplished-by moving the axes46, 49 and; 50,

of each of these electrodes through an angle B relative to the axes, 35, 36 and 37, of their respective bores. When the cathode electrodes are oriented, as shown in FIG. 4, the electron discharge from each to the anode melt 71 define lines along the axes 46, 49 and 50, which when projected onto the melt define tangents to a common circle concentric to the axis 1 of the melt. It has been found that this produces a circular flow of fluid in the melt, which for the orientation shown in FIG. 4 would be clockwise, as viewed in FIG. 4, and this circular flow of fluid in the melt maintains the temperature substantially unidom and the electrode screw carrying the electrode 44 is moveable longitudinally through the ball, by rotating the plastic knob 45 at the end of the screw, it can be seen that the cathode electrode 44 can be moved toward or away from the anode charge 29 and the axis 46, of the electrode 44, can be adjusted so that it crosses the axis 1 of the device or is on either side of it. The other cathode electrode assemblies 33 and 34 are constructed in an identical fashion and have the same latitude of movement as assembly 32, and so the cathode electrodes 47 and 48, for the assemblies 33 and 34, can be positioned with the same facility and in the same manner as cathode electrode 44 and their axes 49 and 50, respectively, can be adjusted to cross axis 1, or lie on either side of axis 1.

Between each of the cathode electrode assemblies 32, 33, and 34, are located assemblies 51, 52 and 53. These window assemblies are identical to each other and preferably spaced between the cathode assemblies. Since the window assemblies are identical in construction, only the one assembly 52 will be described in detail herein. Window assembly 52 consists of a bore 54 through the anode body 27 on an axis 54a, generally directed toward the anode charge 26. Within this bore are located the inside and the outside glass windows 55 and 56, spaced apart by spacer ring 57. The inside window 55 is preferably of high temperature glass, such as quartz, while the outside window 56 may be of lower temperature, colored glass. Window 55 is held between the spacer ring 57 and a gasket 58 against a step on the inside of the bore, and the window 56 is held by retaining ring 59, which holds gasket 61 against window 56. Retaining ring 59 threadedly connects to the bore. f

The pulling mechanism 31 disposed generally along the axis 1 consists of a bore 62, concentric to the axis 1 and machined on the inside to form a socket 63 for containing the ball 64. The mechanism ball 64 is contained in the socket by a gasket 65 secured against the ball by a retaining ring 66, which threads to the inside of the bore. The ball carries the -pulling mechanism screw 67, which threads through the center of the ball and can be screwed in and out of the ball by rotating the knob 68 at the end of the screw. The other end of the pulling mechanism screw has an accommodation for mounting either a sharp-pointed tungsten or molybdenum ingot 69,,or a seed crystal for initiating crystal growth.

In operation, the anode .assembly and cathode electrodes, 42, 45 and 46, are electrically energized so that arcs strike from each of the cathode electrodes to the anode charge 26. These arcs are of sufiicient intensity to melt a portion of the anode charge forming the anode melt 71. The anode melt 71 assumes the shape generally shown in FIG. 1, which is generally globular and is completely contained and supported by the solid anode charge material. Thus, there is no contamination of the melt from a crucible of a foreign material.

FIG. 3 is a sectional view taken as shown in FIG. 1 to illustrate the orientation of the cathode electrodes, 44, 47 and 48, relative to the melt 71 and shows the regular orientation of these electrodes about the melt. FIG. 4

form throughout the melt, and particularly at the center of the melt, from where the crystal body 72 is pulled by the pulling mechanism 31. Quite clearly, if each of the cathode electrodes were tilted relative to the axes of their respective bores, in the opposite direction to that shown in FIG. 4, the circular fiow of fluid in the melt would be counter-clockwise, as viewed in FIG. 4. However, the effect would be the same; the melt would be stirred and temperature throughout the melt would be maintained uniform.

In operation, as the crystal body 72 is pulled from the melt by manipulating the pulling mechanism 31, fresh solid material from the anode charge 29 is fed upward into the melt by raising the piston 23. This is accomplished by turning the sleeve 25.

Some materials are not sufiiciently electrically conductive and it is difiicult, if not impossible, to strike an are even to a melt of such a material. However, if the melt of the material is heated to a suflicient temperature, it becomes sufiiciently electrically conductive to sustain an arc. FIG. 5 illustrates structure and technique for heating and striking an arc to such a material, so that a melt of the material can be produced from which crystals are pulled as grown.

In FIG. 5, Tungsten pins 73, 74 and 75 project from the top of the crucible 21 toward the electrodes 44, 47 and 48, respectively. In operation, arcs are struck between each of these electrodes and the respective tungsten pin so that the arcs are close to the edge of the charge 29 and heat portions 76, 77 and 78 of the charge melt 71. The arcs heat the melt portions 76, 77 and 78 until these portions are sufficiently electrically conductive that arcs will be sustained from the electrodes to the melt for more efiicient heating of the whole melt.

In many applications, it is desirable to provide an atmosphere of inert gas about the melt and the growing crystal in order to prevent the formation of contaminants in the grown crystal from gases in the region 13. The

gas also contributes to the plasma which conducts the arc. These conditions are provided by injecting an inert gas, such as argon, which may contain traces of hydrogen, into the crystal growing region 13, preferably toward the base of the crystal which is grown from the melt. For this purpose, orifices 83 to 88 are provided, which lead from the annular cavity 18 into the region 13 and are directed toward the base of the grown crystal. The orientation of the axes of these orifices 83 to 88 are shown in FIGS. 3 and 4. They preferably define tangents to a circle so that the gas swirls in the region 13 and circulates about the surface of the melt. Particularly good results have been obtained when the direction of the rotation of the swirl of gas is the same as the direction of rotation of the liquid flow in the melt. Accordingly, as shown in FIG. 4, the orifices 83 and 88 preferably are directed along tangent lines in the same circular direction as the cathode electrodes, 44, 47 and 48.

FIG. 6 is a three-quarter view of the completely assembled crystal growing device, described in detail in FIGS. 1 to 4. Anode coolant flow is conducted to the annular cavity 17 in the anode assembly 2, from a source which is not shown, via a pipe 91 and the coolant is returned to the source from the cavity 17, via pipe 92. lInert gas is conducted from another and different source, again which is not shown, to the annular cavity 18 in the anode assembly 2, via a gas pipe 93.

The cathode assembly 3 is also cooled, particularly the cathode electrode pivot balls, such as pivot ball 39, and the glass windows such as 55 and 56. For this purpose, liquid coolant is conducted to the cathode block by pipe 94, and conducted throughout the block by passages (not shown) to the space between the cathode pivot ball 39 and bore 38, and the insulating rings 40 and 41. Thus, the cooling fluid circulates around and cools each of the cathode pivot balls. Cooling fluid leakage into the region 13 is prevented by ring 41.

Cooling liquid is also conducted within the block to the space between windows and 56 by passages which are not shown and is returned to its source via pipe 95.

DC potentials are applied to the anode assembly 2 and the cathode electrodes, 46, 47 and 48, from a source 96. The most convenient arrangement for energizing the anode body and the cathode electrodes from the standpoint of use and operation of the device by an operator, is to energize the anode assembly 2 at ground potential and to energize the cathode electrodes at a negative DC potential. It is preferred in this arrangement for electrically energizing the cathode electrodes that rings such as 40 and 41, which support the cathode pivot ball 39, are electrically insulating and the negative DC potential is coupled from the source 96 to the electrodes 44, 47 and 48, via rings 97, 98 and 99, respectively, which are attached to the cathode screws. This arrangement permits the cathode electrodes to be separately energized.

In another arrangement, the cathode screws such as screw 43, or the cathode pivot balls, such as ball 39, can be made of electrically insulating material so that the cathodes 44, 47 and 48 would be insulated from the cathode body 30.

With either of these arrangements, the cathode body 30 remains at a non-dangerous potential level and is no hindrance to the operator.

The novel method and structure for growing or pulling crystals described herein is exemplified by the various structures described. With these structures, the melt of material from which the crystals are grown or pulled is contained by the same material in solid form, so that the container does not contaminate the melt and the solid material is contained in a cold crucible. Thus, the anode charge in the description herein, serves the function of the crucible normally used in a typical Czochralski crystal pulling structure, but avoids many of the enumerated disadvantages of the crucibles used in the typical Czochralski structures. In addition, since the anode charge 29 is continuously fed upward by the action of the anode piston 23, the melt 71 at the center of the charge can be most advantageously placed. Furthermore, since the charge material may be in powder form, which is a poor heat conductor, less powder is required than would be required to maintain a melt in the typical heated crucible employed in the past in Czochralski type crystal-pulling structures. In addition, since the anode charge crucible 21 is cooled, there is very little likelihood of its contaminating the solid charge 29, and even less likelihood of its contaminating the anode melt 71.

-C1'ystals can be pulled from the melt 71 employing the pulling mechanism 31 or other structures for this purpose. Other structure can .be substituted for the In the pressure molding technique, a hollow tube is ,7

inserted into the melt 71, alongthe axis 1 from above, and pressure in the region 13 is increased, forcing melt liquid up into the tube, whereupon the arcs are turned off and the melt crystallizes in the tube.

In the drop casting technique, a mold form is substituted for the crucible 21, so that the melt flows by gravity into the mold, whereupon the arcs are turned off and the melt crystallizes in the form of the mold.

The embodiments described herein all incorporate features of the invention which provide a unique mechanism for forming, heating and stirring a melt and for growing crystals from the melt. These structures are but a few incorporating the various features of the invention, which may be used separately or in combination as de scribed, and the specific descriptions are not intended to limit the spirit and scope of the invention set forth in the accompanying claim.

What is claimed is:-

1. A method for growing crystals comprising the steps of,

placing selected semiconductor material in an electrically conductive holder, producing a plurality of arcs between the material and movable electrodes, said electrodes being at a negative potential with respect to the material producing a plurality of arcs between the material and movable electrodes, said electrodes being at a negative potential with respect to the material, said arcs being regularly spaced about the center of said material and of sufficient intensity to produce a melt at said center of a portion of'said material contained by the unmelted portion of said material,

positioning said electrodes so that the projections on said melt of the directions of plasma and electron flow in said arcs define tangent lines to a circle so that electron and plasma flow to the material stirs the melt in a circle and growing crystals from said melt substantially at the center of said circle.

References Cited UNITED STATES PATENTS 2,475,810 7/1949 Theuerer 23-301 2,958,719 11/1960 Beecher 1331 3,012,865 12/1961 Pellin 23-301 3,160,497 12/1964 Loung 23'301 3,224,844 12/ 1965 Gerthsen 23--301 3,279,896 10/1966 Hamilton 23301 3,314,769 4/ 1967 Rudness 23-301 2,825,641 3/1958 Beall et a1. 1O 3,002,320 10/1961 Theuerer 23301 3,160,497 12/1964 Loung 23301 3,472,941 10/ 1969 Floymays 75-10 NORMAN YUDKOFF, Primary Examiner S. SILVERBERG, Assistant Examiner US. Cl. X.R. 219-12 

